%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:15:37 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of clauses : 61 ( 18 unt; 35 nHn; 54 RR)
% Number of literals : 184 ( 12 equ; 74 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 107 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Zorn_OTFin__linear__lemma1_0,axiom,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
cnf(cls_Set_OsubsetD_0,axiom,
( ~ c_lessequals(X2,X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Zorn_OTFin__linear__lemma1_1,axiom,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X1,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
cnf(cls_Zorn_OTFin__linear__lemma1_2,axiom,
( c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3) != X1
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
cnf(cls_conjecture_6,negated_conjecture,
( ~ c_in(X2,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X1,X2,tc_set(tc_set(t_a)))
| X1 = X2
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Zorn_OTFin__linear__lemma1_3,axiom,
( ~ c_lessequals(c_Zorn_Osucc(X2,c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X3),X1,tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
cnf(cls_Zorn_OAbrial__axiom1_0,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
cnf(cls_Set_OsubsetI_1,axiom,
( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(c_0_14,plain,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin__linear__lemma1_0]) ).
cnf(c_0_15,plain,
( ~ c_lessequals(X2,X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3) ),
inference(fof_simplification,[status(thm)],[cls_Set_OsubsetD_0]) ).
cnf(c_0_16,plain,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
c_0_14 ).
cnf(c_0_17,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_1 ).
cnf(c_0_18,plain,
( ~ c_lessequals(X2,X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3) ),
c_0_15 ).
cnf(c_0_19,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
cls_conjecture_0 ).
cnf(c_0_20,plain,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X1,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin__linear__lemma1_1]) ).
cnf(c_0_21,plain,
( c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3) != X1
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin__linear__lemma1_2]) ).
cnf(c_0_22,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X1,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
c_0_20 ).
cnf(c_0_25,plain,
( c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3) != X1
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
c_0_21 ).
cnf(c_0_26,negated_conjecture,
( ~ c_in(X2,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X1,X2,tc_set(tc_set(t_a)))
| X1 = X2
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a))) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_6]) ).
cnf(c_0_27,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
cls_conjecture_3 ).
cnf(c_0_29,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_30,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) != X1
| c_lessequals(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_31,negated_conjecture,
( ~ c_in(X2,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X1,X2,tc_set(tc_set(t_a)))
| X1 = X2
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a))) ),
c_0_26 ).
cnf(c_0_32,negated_conjecture,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_34,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) != X1
| c_lessequals(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_35,plain,
( ~ c_lessequals(c_Zorn_Osucc(X2,c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X3),X1,tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin__linear__lemma1_3]) ).
cnf(c_0_36,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),X1,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = X1 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_39,plain,
( ~ c_lessequals(c_Zorn_Osucc(X2,c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X3),X1,tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
c_0_35 ).
cnf(c_0_40,negated_conjecture,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_28])]),c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X1,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X1,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_23]),c_0_28])]) ).
cnf(c_0_43,negated_conjecture,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_42,c_0_17]) ).
cnf(c_0_44,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
cls_Zorn_OAbrial__axiom1_0 ).
cnf(c_0_45,negated_conjecture,
( ~ c_in(X1,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a))
| c_in(X1,v_n,tc_set(t_a))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_18,c_0_43]) ).
cnf(c_0_46,plain,
( ~ c_in(X1,X3,tc_set(X4))
| c_in(X1,c_Zorn_Osucc(X2,X3,X4),tc_set(X4)) ),
inference(spm,[status(thm)],[c_0_18,c_0_44]) ).
cnf(c_0_47,plain,
( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
inference(fof_simplification,[status(thm)],[cls_Set_OsubsetI_1]) ).
cnf(c_0_48,negated_conjecture,
( ~ c_in(X1,v_x,tc_set(t_a))
| c_in(X1,v_n,tc_set(t_a))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
cls_Set_OsubsetI_0 ).
cnf(c_0_50,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
inference(fof_simplification,[status(thm)],[cls_conjecture_4]) ).
cnf(c_0_51,plain,
( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
c_0_47 ).
cnf(c_0_52,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_x,X1,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(v_x,X1,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
c_0_50 ).
cnf(c_0_54,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
inference(fof_simplification,[status(thm)],[cls_conjecture_5]) ).
cnf(c_0_55,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X1,tc_set(tc_set(t_a)))
| v_n = X1 ),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_56,negated_conjecture,
c_lessequals(v_n,v_x,tc_set(tc_set(t_a))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_57,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
c_0_54 ).
cnf(c_0_58,negated_conjecture,
v_x = v_n,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_28])]),c_0_57]) ).
cnf(c_0_59,plain,
c_lessequals(X1,X1,tc_set(X2)),
inference(spm,[status(thm)],[c_0_51,c_0_49]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_58]),c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.36 % Computer : n004.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8046.5625MB
% 0.13/0.36 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 05:41:49 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45 % Version: 3.5.1
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.45 % Starting sh5l with 300s (1) cores
% 0.13/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2360610 completed with status 0
% 0.13/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.45 % No SInE strategy applied
% 0.13/0.45 % Search class: FGUSF-FFMS32-MFFFFFNN
% 0.13/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2360616 completed with status 0
% 0.13/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.45 % No SInE strategy applied
% 0.13/0.45 % Search class: FGUSF-FFMS32-MFFFFFNN
% 0.13/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.45 % Preprocessing time : 0.001 s
% 0.13/0.45 % Presaturation interreduction done
% 0.13/0.45
% 0.13/0.45 % Proof found!
% 0.13/0.45 % SZS status Unsatisfiable
% 0.13/0.45 % SZS output start CNFRefutation
% See solution above
% 0.13/0.45 % Parsed axioms : 14
% 0.13/0.45 % Removed by relevancy pruning/SinE : 0
% 0.13/0.45 % Initial clauses : 14
% 0.13/0.45 % Removed in clause preprocessing : 0
% 0.13/0.45 % Initial clauses in saturation : 14
% 0.13/0.45 % Processed clauses : 164
% 0.13/0.45 % ...of these trivial : 0
% 0.13/0.45 % ...subsumed : 17
% 0.13/0.45 % ...remaining for further processing : 147
% 0.13/0.45 % Other redundant clauses eliminated : 0
% 0.13/0.45 % Clauses deleted for lack of memory : 0
% 0.13/0.45 % Backward-subsumed : 19
% 0.13/0.45 % Backward-rewritten : 19
% 0.13/0.45 % Generated clauses : 352
% 0.13/0.45 % ...of the previous two non-redundant : 334
% 0.13/0.45 % ...aggressively subsumed : 0
% 0.13/0.45 % Contextual simplify-reflections : 2
% 0.13/0.45 % Paramodulations : 352
% 0.13/0.45 % Factorizations : 0
% 0.13/0.45 % NegExts : 0
% 0.13/0.45 % Equation resolutions : 0
% 0.13/0.45 % Disequality decompositions : 0
% 0.13/0.45 % Total rewrite steps : 69
% 0.13/0.45 % ...of those cached : 54
% 0.13/0.45 % Propositional unsat checks : 0
% 0.13/0.45 % Propositional check models : 0
% 0.13/0.45 % Propositional check unsatisfiable : 0
% 0.13/0.45 % Propositional clauses : 0
% 0.13/0.45 % Propositional clauses after purity: 0
% 0.13/0.45 % Propositional unsat core size : 0
% 0.13/0.45 % Propositional preprocessing time : 0.000
% 0.13/0.45 % Propositional encoding time : 0.000
% 0.13/0.45 % Propositional solver time : 0.000
% 0.13/0.45 % Success case prop preproc time : 0.000
% 0.13/0.45 % Success case prop encoding time : 0.000
% 0.13/0.45 % Success case prop solver time : 0.000
% 0.13/0.45 % Current number of processed clauses : 95
% 0.13/0.45 % Positive orientable unit clauses : 19
% 0.13/0.45 % Positive unorientable unit clauses: 0
% 0.13/0.45 % Negative unit clauses : 0
% 0.13/0.45 % Non-unit-clauses : 76
% 0.13/0.45 % Current number of unprocessed clauses: 192
% 0.13/0.45 % ...number of literals in the above : 807
% 0.13/0.45 % Current number of archived formulas : 0
% 0.13/0.45 % Current number of archived clauses : 52
% 0.13/0.45 % Clause-clause subsumption calls (NU) : 2258
% 0.13/0.45 % Rec. Clause-clause subsumption calls : 944
% 0.13/0.45 % Non-unit clause-clause subsumptions : 38
% 0.13/0.45 % Unit Clause-clause subsumption calls : 178
% 0.13/0.45 % Rewrite failures with RHS unbound : 0
% 0.13/0.45 % BW rewrite match attempts : 50
% 0.13/0.45 % BW rewrite match successes : 4
% 0.13/0.45 % Condensation attempts : 0
% 0.13/0.45 % Condensation successes : 0
% 0.13/0.45 % Termbank termtop insertions : 17356
% 0.13/0.45 % Search garbage collected termcells : 38
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.013 s
% 0.13/0.45 % System time : 0.005 s
% 0.13/0.45 % Total time : 0.018 s
% 0.13/0.45 % Maximum resident set size: 3388 pages
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.050 s
% 0.13/0.45 % System time : 0.020 s
% 0.13/0.45 % Total time : 0.070 s
% 0.13/0.45 % Maximum resident set size: 4608 pages
% 0.13/0.45 % E exiting
%------------------------------------------------------------------------------